Ejournal 2: “Making life more complicated with complex numbers”

COMPLEX NUMBERS

Although the name sounds intimidating, it really isn’t once you get used to it. Generally we can separate numbers into two broad categories: real numbers and imaginary numbers. Some of you may have never heard about imaginary numbers, but I’m sure most of you are familiar with real numbers as these are the numbers we deal with in our daily lives and use most of the time.

• 

An imaginary number is the square root of -1, suitably called so as in the real numbers system, inputting this into a calculator would have resulted in math error as it is not possible to compute that. Based on imaginary numbers we can create numerous more numbers such as 5i, -12i etc. These are all examples of pure imaginary numbers. Well, what about numbers such as -2 + 3i? This gives rise to complex number, which is a number that can be represented in the form a + bi, where a and b are real numbers and i is the square root of -1. It is a complex number as it is neither a real nor an imaginary number.

Another interesting thing to note is that all real numbers and imaginary numbers are complex numbers as well, but not all complex numbers are real numbers/pure imaginary numbers. This is because a real number such as 5 can be represented as 5 + 0i, and an imaginary number such as 3i can be represented as 0 + 3i.

APPLICATIONS IN OUR LIVES

Although we may not be able to think of the use of complex numbers in our daily lives, some people do encounter these numbers often and without complex numbers, many of the things we encounter or use everyday would not be possible. Complex numbers are used especially in jobs requiring the field of physics and math. Here are some of the applications:

1. Most of us – especially the ones who are able to read this blog – are lucky enough to have access to electricity and power. This electricity comes from generators in power stations, and these generators use the concept of electromagnetism and require some knowledge of electrical engineering.

Both of these fields require as in electricity, one of the units we use is the unit Voltage which is usually represented as V = V0 (cos wt + j sin wt), where j is complex to find the difference between real and reactive power in a system. Real Power is power which results in active work. In other words, active power is solely that work which is done for producing of real (useful) work in this case electricity. Whereas Reactive Power can be stated as “The power which is required to establish and maintain a magnetic field”, which helps produce the electricity, but is not the power which is directly turned into electricity.

2. Robots are also built and programmed with the help of complex numbers. Control systems – which use complex numbers – are used to make these robots by figuring out if the system is stable or not.

3. Another use of complex numbers is in signal processing. Signals are useful in cellular technology (the technology our phones use), radar and wireless technologies such as radios. Even more surprising is that they can be used in even biology when studying brain waves.

IB LEARNER PROFILE

The first IB Learner Profile which resonates with me while typing up this blog post is caring, because I have developed a sense of respect towards people whose occupation deals with complex numbers (as we can see that it is not an easy thing to comprehend). Doing complex numbers at an IB level makes me feel like the person in the meme below, so it’s almost unfathomable for me to know that there are people whose occupation relies heavily on this topic.

Another learner profile that I found myself relating to is knowledgeable as through this blog post, it really pushed myself to find and understand various uses of complex numbers as I originally could not imagine where it would be applicable. This has really widened my horizons and made me more aware of how the same math is used locally and globally. It amazes me that even though people live all over the world in different countries speaking in different languages, the same math is being used.

The last learner profile that kept popping up in my mind while writing this is reflective, as I had to think about where I might possibly encounter and experience the use of complex numbers. Even though I was unable to think of an application where I personally used complex numbers, I could find things I use on a day-to-day basis that relied on the concept of complex numbers. It made me ponder on my daily routine and realize that there are probably a lot more ways in which math is involved in my daily life, whether I know it or not.

REFERENCES

https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-num/a/intro-to-complex-numbers

https://www.quora.com/What-are-some-real-life-applications-of-complex-numbers-in-engineering-and-practical-life

https://www.livescience.com/42748-imaginary-numbers.html

https://www.quora.com/What-is-real-reactive-and-apparent-power